comparison scripts/ABSapproxSingle.py @ 32:e1da5140c9a5

Count and display finished jobs in run_once_tuple()
Disabled "dictionary not normalized" message in OMP
Fixed bug that displayed same values for all algorithms
Made TST default iterations nsweep = 300

+# -*- coding: utf-8 -*-
+"""
+Created on Sat Nov 05 18:08:40 2011
+
+@author: Nic
+"""
+
+import numpy as np
+import scipy.io
+import math
+doplot = True
+try: 
+  import matplotlib.pyplot as plt
+except:
+  doplot = False
+if doplot:  
+  import matplotlib.cm as cm
+import pyCSalgos
+import pyCSalgos.GAP.GAP
+import pyCSalgos.SL0.SL0_approx
+
+# Define functions that prepare arguments for each algorithm call
+def run_gap(y,M,Omega,epsilon):
+  gapparams = {"num_iteration" : 1000,\
+                   "greedy_level" : 0.9,\
+                   "stopping_coefficient_size" : 1e-4,\
+                   "l2solver" : 'pseudoinverse',\
+                   "noise_level": epsilon}
+  return pyCSalgos.GAP.GAP.GAP(y,M,M.T,Omega,Omega.T,gapparams,np.zeros(Omega.shape[1]))[0]
+ 
+def run_sl0(y,M,Omega,D,U,S,Vt,epsilon,lbd):
+  
+  N,n = Omega.shape
+  #D = np.linalg.pinv(Omega)
+  #U,S,Vt = np.linalg.svd(D)
+  aggDupper = np.dot(M,D)
+  aggDlower = Vt[-(N-n):,:]
+  aggD = np.concatenate((aggDupper, lbd * aggDlower))
+  aggy = np.concatenate((y, np.zeros(N-n)))
+  
+  sigmamin = 0.001
+  sigma_decrease_factor = 0.5
+  mu_0 = 2
+  L = 10
+  return pyCSalgos.SL0.SL0_approx.SL0_approx(aggD,aggy,epsilon,sigmamin,sigma_decrease_factor,mu_0,L)
+
+def run_bp(y,M,Omega,D,U,S,Vt,epsilon,lbd):
+  
+  N,n = Omega.shape
+  #D = np.linalg.pinv(Omega)
+  #U,S,Vt = np.linalg.svd(D)
+  aggDupper = np.dot(M,D)
+  aggDlower = Vt[-(N-n):,:]
+  aggD = np.concatenate((aggDupper, lbd * aggDlower))
+  aggy = np.concatenate((y, np.zeros(N-n)))
+  
+  sigmamin = 0.001
+  sigma_decrease_factor = 0.5
+  mu_0 = 2
+  L = 10
+  return pyCSalgos.SL0.SL0_approx.SL0_approx(aggD,aggy,epsilon,sigmamin,sigma_decrease_factor,mu_0,L)
+
+
+# Define tuples (algorithm setup function, algorithm function, name)
+gap = (run_gap, 'GAP')
+sl0 = (run_sl0, 'SL0_approx')
+
+# Define which algorithms to run
+#  1. Algorithms not depending on lambda
+algosN = gap,   # tuple
+#  2. Algorithms depending on lambda (our ABS approach)
+algosL = sl0,   # tuple
+
+def mainrun():
+  
+  nalgosN = len(algosN)  
+  nalgosL = len(algosL)
+  
+  #Set up experiment parameters
+  d = 50.0;
+  sigma = 2.0
+  #deltas = np.arange(0.05,1.,0.05)
+  #rhos = np.arange(0.05,1.,0.05)
+  deltas = np.array([0.05, 0.45, 0.95])
+  rhos = np.array([0.05, 0.45, 0.95])
+  #deltas = np.array([0.05])
+  #rhos = np.array([0.05])
+  #delta = 0.8;
+  #rho   = 0.15;
+  numvects = 100; # Number of vectors to generate
+  SNRdb = 20.;    # This is norm(signal)/norm(noise), so power, not energy
+  # Values for lambda
+  #lambdas = [0 10.^linspace(-5, 4, 10)];
+  #lambdas = np.concatenate((np.array([0]), 10**np.linspace(-5, 4, 10)))
+  lambdas = np.array([0., 0.0001, 0.01, 1, 100, 10000])
+
+  meanmatrix = dict()
+  for i,algo in zip(np.arange(nalgosN),algosN):
+    meanmatrix[algo[1]]   = np.zeros((rhos.size, deltas.size))
+  for i,algo in zip(np.arange(nalgosL),algosL):
+    meanmatrix[algo[1]]   = np.zeros((lambdas.size, rhos.size, deltas.size))
+  
+  for idelta,delta in zip(np.arange(deltas.size),deltas):
+    for irho,rho in zip(np.arange(rhos.size),rhos):
+      
+      # Generate data and operator
+      Omega,x0,y,M,realnoise = genData(d,sigma,delta,rho,numvects,SNRdb)
+      
+      # Run algorithms
+      print "***** delta = ",delta," rho = ",rho
+      mrelerrN,mrelerrL = runonce(algosN,algosL,Omega,y,lambdas,realnoise,M,x0)
+      
+      for algotuple in algosN: 
+        meanmatrix[algotuple[1]][irho,idelta] = 1 - mrelerrN[algotuple[1]]
+        if meanmatrix[algotuple[1]][irho,idelta] < 0 or math.isnan(meanmatrix[algotuple[1]][irho,idelta]):
+          meanmatrix[algotuple[1]][irho,idelta] = 0
+      for algotuple in algosL:
+        for ilbd in np.arange(lambdas.size):
+          meanmatrix[algotuple[1]][ilbd,irho,idelta] = 1 - mrelerrL[algotuple[1]][ilbd]
+          if meanmatrix[algotuple[1]][ilbd,irho,idelta] < 0 or math.isnan(meanmatrix[algotuple[1]][ilbd,irho,idelta]):
+            meanmatrix[algotuple[1]][ilbd,irho,idelta] = 0
+   
+  #  # Prepare matrices to show
+  #  showmats = dict()
+  #  for i,algo in zip(np.arange(nalgosN),algosN):
+  #    showmats[algo[1]]   = np.zeros(rhos.size, deltas.size)
+  #  for i,algo in zip(np.arange(nalgosL),algosL):
+  #    showmats[algo[1]]   = np.zeros(lambdas.size, rhos.size, deltas.size)
+
+    # Save
+    tosave = dict()
+    tosave['meanmatrix'] = meanmatrix
+    tosave['d'] = d
+    tosave['sigma'] = sigma
+    tosave['deltas'] = deltas
+    tosave['rhos'] = rhos
+    tosave['numvects'] = numvects
+    tosave['SNRdb'] = SNRdb
+    tosave['lambdas'] = lambdas
+    try:
+      scipy.io.savemat('ABSapprox.mat',tosave)
+    except TypeError:
+      print "Oops, Type Error"
+      raise    
+  # Show
+  if doplot:
+    for algotuple in algosN:
+      plt.figure()
+      plt.imshow(meanmatrix[algotuple[1]], cmap=cm.gray, interpolation='nearest',origin='lower')
+    for algotuple in algosL:
+      for ilbd in np.arange(lambdas.size):
+        plt.figure()
+        plt.imshow(meanmatrix[algotuple[1]][ilbd], cmap=cm.gray, interpolation='nearest',origin='lower')
+    plt.show()
+  print "Finished."
+  
+def genData(d,sigma,delta,rho,numvects,SNRdb):
+
+  # Process parameters
+  noiselevel = 1.0 / (10.0**(SNRdb/10.0));
+  p = round(sigma*d);
+  m = round(delta*d);
+  l = round(d - rho*m);
+  
+  # Generate Omega and data based on parameters
+  Omega = pyCSalgos.GAP.GAP.Generate_Analysis_Operator(d, p);
+  # Optionally make Omega more coherent
+  U,S,Vt = np.linalg.svd(Omega);
+  Sdnew = S * (1+np.arange(S.size)) # Make D coherent, not Omega!
+  Snew = np.vstack((np.diag(Sdnew), np.zeros((Omega.shape[0] - Omega.shape[1], Omega.shape[1]))))
+  Omega = np.dot(U , np.dot(Snew,Vt))
+
+  # Generate data  
+  x0,y,M,Lambda,realnoise = pyCSalgos.GAP.GAP.Generate_Data_Known_Omega(Omega, d,p,m,l,noiselevel, numvects,'l0');
+  
+  return Omega,x0,y,M,realnoise
+
+def runonce(algosN,algosL,Omega,y,lambdas,realnoise,M,x0):
+  
+  d = Omega.shape[1]  
+  
+  nalgosN = len(algosN)  
+  nalgosL = len(algosL)
+  
+  xrec = dict()
+  err = dict()
+  relerr = dict()
+
+  # Prepare storage variables for algorithms non-Lambda
+  for i,algo in zip(np.arange(nalgosN),algosN):
+    xrec[algo[1]]   = np.zeros((d, y.shape[1]))
+    err[algo[1]]    = np.zeros(y.shape[1])
+    relerr[algo[1]] = np.zeros(y.shape[1])
+  # Prepare storage variables for algorithms with Lambda    
+  for i,algo in zip(np.arange(nalgosL),algosL):
+    xrec[algo[1]]   = np.zeros((lambdas.size, d, y.shape[1]))
+    err[algo[1]]    = np.zeros((lambdas.size, y.shape[1]))
+    relerr[algo[1]] = np.zeros((lambdas.size, y.shape[1]))
+  
+  # Run algorithms non-Lambda
+  for iy in np.arange(y.shape[1]):
+    for algofunc,strname in algosN:
+      epsilon = 1.1 * np.linalg.norm(realnoise[:,iy])
+      xrec[strname][:,iy] = algofunc(y[:,iy],M,Omega,epsilon)
+      err[strname][iy]    = np.linalg.norm(x0[:,iy] - xrec[strname][:,iy])
+      relerr[strname][iy] = err[strname][iy] / np.linalg.norm(x0[:,iy])
+  for algotuple in algosN:
+    print algotuple[1],' : avg relative error = ',np.mean(relerr[strname])  
+
+  # Run algorithms with Lambda
+  for ilbd,lbd in zip(np.arange(lambdas.size),lambdas):
+    for iy in np.arange(y.shape[1]):
+      D = np.linalg.pinv(Omega)
+      U,S,Vt = np.linalg.svd(D)
+      for algofunc,strname in algosL:
+        epsilon = 1.1 * np.linalg.norm(realnoise[:,iy])
+        gamma = algofunc(y[:,iy],M,Omega,D,U,S,Vt,epsilon,lbd)
+        xrec[strname][ilbd,:,iy] = np.dot(D,gamma)
+        err[strname][ilbd,iy]    = np.linalg.norm(x0[:,iy] - xrec[strname][ilbd,:,iy])
+        relerr[strname][ilbd,iy] = err[strname][ilbd,iy] / np.linalg.norm(x0[:,iy])
+    print 'Lambda = ',lbd,' :'
+    for algotuple in algosL:
+      print '   ',algotuple[1],' : avg relative error = ',np.mean(relerr[strname][ilbd,:])
+
+  # Prepare results
+  mrelerrN = dict()
+  for algotuple in algosN:
+    mrelerrN[algotuple[1]] = np.mean(relerr[algotuple[1]])
+  mrelerrL = dict()
+  for algotuple in algosL:
+    mrelerrL[algotuple[1]] = np.mean(relerr[algotuple[1]],1)
+  
+  return mrelerrN,mrelerrL
+  
+# Script main
+if __name__ == "__main__":
+
+  #import cProfile
+  #cProfile.run('mainrun()', 'profile')    
+  mainrun()